An arbitrary topology surface can be three dimensionally characterized by descriptions of vertices on the surface and their connectivity. The detail of the surface depends on the number of points that are described, and the amount of information describing each point.
The amount of information describing these models can be extensive. The information, however, can be compressed to reduce some of the load. Compression in general is a tradeoff between accuracy and bit rate, i.e., bits per vertex. This tradeoff is captured in rate-distortion curves.
Rate-distortion curves require the computation of errors or “distortion” between the original surface and a surface that has been estimated. For geometry, an error may be computed using techniques that measure the distance between the geometric shapes. The original and compressed meshes may have very different sample locations and connectivity. Progressive compression provides an early, coarse approximation of the geometry. This is subsequently improved through additional information.